A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

BOUND-CONSTRAINED MINIMIZATION PROBLEMS MARY ANN BRANCH , THOMAS F. COLEMAN AND YUYING LI Abstract. A subspace adaptation of the Coleman-Li trust region and interior method is proposed for solving large-scale bound-constrained minimization problems. This method can be implemented with either sparse Cholesky factorization or conjugate gradient computation. Under reasonable conditions the convergence properties of this subspace trust region method are as strong as those of its full-space version. Computational performance on various large-scale test problems are reported; advantages of our approach are demonstrated. Our experience indicates our proposed method represents an efficient way to solve large-scale bound-constrained minimization problems.